Aiming at the disadvantages of limited adaptive ability and high local shackles probability of marine predators algorithm, a phased-improvement marine predators algorithm is proposed. The differential evolution is implemented in the high velocity ratio phase, which expands the global exploration range with the variation and crossover of the original prey population, and optimize the individual quality seriatim. The sine and cosine algorithm is introduced in the unit velocity phase to fluctuate the parallel architecture with an equal probablity, which is used to improve the flexibility of the Levy flight group and the Brownian motion group, and promote the penetration between groups in order to optimize the development and exploration capabilities of the algorithm in the same rhythm. The Cauchy mutation strategy and the reverse learning strategy are combined in the low velocity ratio phase to evolve the predators into the self-regulation Cauchy mirror predators, for avoiding excessive population assimilation at the end of iteration, so that the anti precocity ability of the algorithm is strengthened. The performance of the improved algorithm is evaluated by the benchmark function comparison optimization experiments and the Wilcoxon's sign rank test, and the results verify that the phased-improvement strategy contributes to the overall expressiveness of the algorithm. The improved algorithm is used to optimize the paraments of online sequential extreme learning machine and applied to transformer fault diagnosis, and the effectiveness and engineering practicability of the phased-improvement strategy are further verified.